In geometry, the volume is defined as the measure of space occupied by a three-dimensional body. The volume of a three-dimensional body is a numerical characteristic of the body; in the simplest case, when the body can be decomposed into a finite set of unit cubes (i.e., cubes with edges of unit length), it is equal to the number of these cubes. Volumes of three-dimensional bodies (i.e., sets in three-dimensional Euclidean space) for which volume can be defined have properties analogous to those of areas of plane figures:

  1. volume is non-negative;
  2. volume is additive (the volume of the union of two bodies is the sum of their volumes);
  3. volume is invariant for displacements;
  4. the volume of the unit cube is equal to one.

Related keywords

  • Specific volume
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